Cooper, 37, and Saldana, 33, who were first spotted getting cozy in January, costar in The Words where their chemistry can be seen on screen.
While promoting the film at Sundance in January, an onlooker told PEOPLE they were "being very affectionate." Then in February, Saldana was photographed spending time with Cooper's mom, Gloria.

In the film Cooper – who was named PEOPLE's 2011 Sexiest Man Alive – plays Rory, a writer who takes credit for another man's literary success.